1. Factoring by GCF

2. Factoring Put the expression in a division tower Continue to divide by numbers or variables until there is no number or variable common to all terms. Put the numbers and variables along the side on the outside of the parentheses. Put the top expression on the inside of parentheses.

3. Example 1 56x 4 – 32x 3 – 72x 2

4. Factor each expression. A. 5(x + 2) + 3x(x + 2) 5(x + 2) + 3x(x + 2) (x + 2)(3x + 5) The terms have a common binomial factor of (x + 2). Factor out (x + 2). B. – 2b(b 2 + 1)+ (b 2 + 1) – 2b(b 2 + 1) + (b 2 + 1) – 2b(b 2 + 1) + 1(b 2 + 1) (b 2 + 1)( – 2b + 1) The terms have a common binomial factor of (b 2 + 1). (b 2 + 1) = 1(b 2 + 1) Factor out (b 2 + 1). Example 2: Factoring Out a Common Binomial Factor

5. Example 3: Factoring by Grouping Factor each polynomial by grouping. Check your answer. 6h 4 – 4h 3 + 12h – 8 (6h 4 – 4h 3 ) + (12h – 8) 2h 3 (3h – 2) + 4(3h – 2) 2(3h – 2)(h 3 + 2) Group terms that have a common number or variable as a factor. Factor out the GCF of each group. (3h – 2) is another common factor. Factor out (3h – 2).

6. Example 4: Factoring by Grouping Factor each polynomial by grouping. Check your answer. 5y 4 – 15y 3 + y 2 – 3y (5y 4 – 15y 3 ) + (y 2 – 3y) 5y 3 (y – 3) + y(y – 3) y(y – 3)(5y 2 + 1) Group terms. Factor out the GCF of each group. (y – 3) is a common factor. Factor out (y – 3).

7. Example 5: Factoring with Opposites Factor 2x 3 – 12x 2 + 18 – 3x 2x 3 – 12x 2 + 18 – 3x (2x 3 – 12x 2 ) + (18 – 3x) 2x 2 (x – 6) + 3(6 – x) 2x 2 (x – 6) + 3( – 1)(x – 6) 2x 2 (x – 6) – 3(x – 6) (x – 6)(2x 2 – 3) Group terms. Factor out the GCF of each group. Simplify. (x – 6) is a common factor. Factor out (x – 6). Write (6 – x) as –1(x – 6).

8. Example 6 Factor each polynomial. Check your answer. 15x 2 – 10x 3 + 8x – 12 (15x 2 – 10x 3 ) + (8x – 12) 5x 2 (3 – 2x) + 4(2x – 3) 5x 2 (3 – 2x) + 4( – 1)(3 – 2x) 5x 2 (3 – 2x) – 4(3 – 2x) -1(2x - 3)(5x 2 – 4) Group terms. Factor out the GCF of each group. Simplify. (3 – 2x) is a common factor. Factor out (3 – 2x). Write (2x – 3) as –1(3 – 2x).

9. Try these… Factor each polynomial. Check your answer. 1. 16x + 20x 3 2. 4m 4 – 12m 2 + 8m Factor each expression. 3. 7k(k – 3) + 4(k – 3) 4. 3y(2y + 3) – 5(2y + 3) (2y + 3)(3y – 5) (k – 3)(7k + 4) 4m(m 3 – 3m + 2) 4x(4 + 5x 2 )

10. Try these (cont)… Factor each polynomial by grouping. Check your answer. 5. 2x 3 + x 2 – 6x – 3 6. 7p 4 – 2p 3 + 63p – 18 7. A rocket is fired vertically into the air at 40 m/s. The expression –5t 2 + 40t + 20 gives the rocket’s height after t seconds. Factor this expression. –5(t 2 – 8t – 4) (7p – 2)(p 3 + 9) (2x + 1)(x 2 – 3)